Problem 70 - Elementary Algebra

Question

It was reported that a flu epidemic is affecting six out of every ten college students in a certain part of the country. At this rate, how many students in that part of the country would be affected at a university of 15,000 students?

Step-by-Step Solution

Answer

9,000 students would be affected.

Step 1: Determine the Rate of Affected Students

The problem states that six out of every ten students are affected. This gives us a rate or proportion of affected students as a fraction, which is \( \frac{6}{10} \). This can be simplified to \( 0.6 \).

Step 2: Calculate the Total Number of Affected Students

To find the total number of affected students at the university, multiply the total number of students by the proportion of affected students: \( 15000 \times 0.6 = 9000 \).

Step 3: Conclusion

With the rate calculated in Step 1 and applying it in Step 2, we find that a total of 9,000 students would be affected at a university with 15,000 students.

Key Concepts

Flu Epidemic Statistics

Understanding flu epidemic statistics is crucial for grasping how the flu can impact large groups of people, like students in a university setting. In this scenario, a flu epidemic is striking six out of every ten students.
This is the same as saying 60% of the student body is at risk. Statistics such as these help public health officials allocate resources effectively, such as vaccines or healthcare personnel.

• "Epidemic" refers to a widespread occurrence of an infectious disease in a community at a particular time.
• By applying simple proportions, we're able to estimate how significant the epidemic could be within a specified group.

Knowing how to interpret such data is key. It allows us to anticipate how many people need support or preventative measures.

Multiplying Proportions

Calculating how many students are affected by multiplying proportions is a straightforward application of mathematical proportions.
The given rate in this problem, six out of ten, is expressed as the fraction \( \frac{6}{10} \), which represents 60% or 0.6 when converted to a decimal.

• Multiply the total number of students by this decimal to find the number impacted. In this context, it's \( 15000 \times 0.6 \).
• This step requires an understanding that multiplication of proportions will give us the part of the whole associated with the proportion.

In essence, multiplying proportions provides a powerful way to determine the impact of percentages on larger numbers.

Simplifying Fractions

Simplifying fractions helps us work with more manageable numbers and can be essential for making complex calculations easier. Initially, the problem provides the fraction \( \frac{6}{10} \).
Simplifying involves reducing this fraction by finding a common factor of both the numerator (the top number) and the denominator (the bottom number).

• In \( \frac{6}{10} \), the greatest common factor is 2.
• Divide both the numerator and denominator by 2, resulting in the simplified fraction \( \frac{3}{5} \).

When converted into a decimal, \( \frac{3}{5} \) equals 0.6.
Whether you're working with large statistical data or solving day-to-day math problems, simplifying fractions into decimals makes them easier to apply and understand.